A way of increasing manometer sensitivity is to use a twoflu

A way of increasing manometer sensitivity is to use a two-fluid version as illustrated. For this type of manometer, derive an equation for the pressure difference (P_A- P_B) in terms of h, g, p_1 and p_2. What must you consider in selection of the two fluids to obtain maximum sensitivity?

Solution

Here , for the pressure difference ,

as the pressure in both tubes is same at the same height

for the pressure at the bottom

PA + p1 * g * h = PB + p2 * g * h

PA - PB = (p2 - p1) * g * h

the pressure difference is (p2 - p1) * g * h

for manometer to be sensitive

(p2 - p1) should be a large value

hence , p2 must be very greater than p1

fluid 1 can be air , and 2 can be water